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This article represents Legendre spectral collocation method based on Legendre polynomials to solve a stochastic Susceptible, infected, Recovered (SIR) model. The Legendre polynomials on stochastic SIR model that convert it to a system of equations has been applied and then solved by the Legendre spectral method, which leads to excellent accuracy and convergence by implementing Legendre–Gauss–Lobatto collocation points permitting to generate coarser meshes. The numerical results for both the deterministic and stochastic models are presented. In case of probably small noise, the verge dynamics is analyzed. The large noise will show eradication of disease, which controls disease spreading. Various graphical results demonstrate the effectiveness of the proposed method to SIR model.